A342430 -id:A342430 - cp's OEIS frontend

A380455 Maximum number of prime polyomino factors of an n-polyomino.

1, 1, 1, 1, 3, 1, 4, 1, 5, 1, 5, 1

Offset: 2

Gordon Hamilton, Jun 22 2025

Grade one students are capable of understanding "prime" and "composite" and "is a factor of" when presented in terms of polyomino tilings. Exploring these ideas is a 10/10 classroom activity, even if limited to only pentomino factors of larger polyominoes.

Conjectured terms: a(14)..a(17) = 10?, 3, 12?, 1.

			a(6) = 3 because the 2x3 rectangular hexomino can be tiled by three prime polyominoes:
The domino:
  XOY
  XOY
The bent tromino:
  XXO
  XOO
The straight tromino:
  XXX
  OOO
a(9) = 1 because no 9-polyomino can be tiled by both all straight and all bent trominoes.
It is conjectured that a(14) = 10 because this 14-polyomino can be tiled with 9 prime heptominoes and by the domino:
    X
   XXXX
   XXXX
   XXXX
     X
It is also conjectured that a(16) = 12 because this 16-polyomino can be tiled with twelve prime 8-polyominoes:
     XXX
    XXXXX
   XXXXX
    XXX

Cf. A342430 (number of prime polyominoes with n cells).

a(p) = 1 if p is prime. - Pontus von Brömssen, Jun 24 2025

cp's OEIS Frontend

A380455 Maximum number of prime polyomino factors of an n-polyomino.

Views

Author

Keywords

Comments

Examples

Crossrefs

Formula